Beyond Perturbation: Introduction to the Homotopy Analysis Method

By Shijun Liao, S. Sherif. 2003

3,359 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/0a78d3a54c8074e0aeb5b890d7bb29500e6c9063

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Citations in the corpus

Mixed Convective Heat Transfer for MHD Viscoelastic Fluid Flow over a Porous Wedge with Thermal Radiation (2014, methodology): “HAM was employed by Liao, who was the first to offer a general analytical method for nonlinear problems [20, 21].”
Approximate Analytical Solution to Time-Fractional Damped Burger and Cahn-Allen Equations (2013, neutral): “(2) In a similar way to integer-order differentiations, Caputo ’s fractional differentiation is also a linear operation Dα(λ f (x)+μg(x)) = λDα f (x)+μDαg(x), where λ and μ are constants.”
Key words: Nonlinear Differential-Difference Equations; Exp-Function Method; N-Soliton Solutions (2010, methodology): “A complete review for the convergence discussion is available in [49].”
Comparison between the HAM and HPM solutions of thin film flows of non-Newtonian fluids on a moving belt (2007, methodology): “Due to this fact in mind, Liao [11, 12 ] has recently developed a technique namely the homotopy analysis method which does not require small parameters and thus can be used to solve non-linear problems in science and engineering which have no small or large parameters.”
THE APPLICATION OF HOMOTOPY ANALYSIS METHOD TO NONLINEAR EQUATIONS ARISING IN HEAT TRANSFER (2006, methodology): “This rule, so-called rule of coefficient ergodicity by Liao, [13].”
Optimal execution with non-linear transient market impact (2014, methodology): “which is one of the solutions of the original nonlinear equation, as proved by Liao [32].”